Certain events are dependent on the convergence of at least two natural phenomena having distinct periods that are not multiples of one another. Sunrise and sunset times, which depend, at a given point, on the time and date or on tide times and tidal coefficients, which depend, in addition, on the position of the moon, can be mentioned as examples. Representing such events by using exclusively mechanical means presents some difficulty.
A first mechanical solution for representing an event that depends on two-time functions, could consist in using a three-dimensional cam. The three-dimensional cam may, for example, be independently movable in the two degrees of freedom of a sliding pivot. The feeler moves in reference to the cam surface, in rotation about the pivot axis and in translation along the axis, each of the two movements being determined independently according to the two time functions. However, this type of solution is unsuitable for incorporation into a timepiece mechanism due to the excessive space occupied by the three-dimensional cam.
WO Patent Application No 2016/029296 proposes performing various mathematical operations, including multiplication, but without detailing the embodiment that allows this object to be achieved.